Timeline for A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
Current License: CC BY-SA 4.0
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| Jun 17, 2020 at 17:50 | comment | added | whuber♦ | @Aksakal I'm not the one to address that comment to. I have already protested that "Soviet" is not an adjective I am using. | |
| Jun 17, 2020 at 17:47 | comment | added | Aksakal | @whuber, is there such a thing as "soviet data"? I think Soviets were always manipulating statistics. Whether post Soviet countries keep this tradition it is a question to me. Almost everyone who I know and still lives over there would assert that it's still the case. I don't have the first hand experience though with recent stats. I highly suspect any and all COVID related data from the region at least through April. At the moment it is probably impossible to hide the spread | |
| S May 23, 2020 at 23:12 | history | suggested | Walt Stoneburner | CC BY-SA 4.0 |
fixed various typos
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| May 23, 2020 at 22:27 | review | Suggested edits | |||
| S May 23, 2020 at 23:12 | |||||
| May 23, 2020 at 17:52 | comment | added | whuber♦ | @Alexey Thank you for the explanation. | |
| May 23, 2020 at 17:41 | comment | added | alexeymosco | @whuber, sir, I did it for one purpose only. "@Arkasal: That is some very Soviet data. – Ben - Reinstate Monica yesterday " The response to this comment under the Question. No other purposes. | |
| May 23, 2020 at 17:32 | comment | added | Sextus Empiricus | The question about the Poissonness of the data is sort of also a question about whether or not these data are supposed to relate to what 'the virus determines' (the alternative is that the data reflects measurement and reporting capabilities, and this is a likely scenario if you compare the different countries with enormous heterogeneity in approaches and figures). None of these statistics are realistic (independent from dispersion) and all of them require some clear descriptions of limitations. Except Iceland, which tests extremely a lot, all these data are just tips of the virus-icebergs. | |
| May 23, 2020 at 17:23 | comment | added | Sextus Empiricus | @whuber 'soviet-style manipulations' is a response to 'soviet data'. That latter one is a characterisation that was not started by Alexey. | |
| May 23, 2020 at 17:17 | comment | added | whuber♦ | Re "Soviet-style manipulations:" a search of this Web page shows you are the sole person even referring to such a claim! I think most, if not all, of the posters and readers on this page understand the limitations of statistical analysis and wouldn't presume that an unrealistic-looking dataset necessarily indicates there was skullduggery at work. Your arguments about non-Poissonness really don't hit home, because ultimately the virus determines who gets sick and when; and that is going to be close to Poisson. This is the basic process driving everything else. | |
| May 23, 2020 at 17:11 | comment | added | Aksakal | It’s clearly not poisson but it’s not the point. The point is that the dispersion is too small. | |
| May 23, 2020 at 16:03 | history | edited | alexeymosco | CC BY-SA 4.0 |
edit layout
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| May 23, 2020 at 15:22 | comment | added | alexeymosco | @Aksakal, I added mor argumentation why I think these data are not Poisson in nature. Bullet in my answer 1.1) | |
| May 23, 2020 at 15:21 | history | edited | alexeymosco | CC BY-SA 4.0 |
added more arguments
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| May 23, 2020 at 15:10 | comment | added | alexeymosco | @EngrStudent, "I respect Russian mathematics greatly. I don't know about Russian economics either way though". I was tired yesterday, sorry. On Russian math, recall the names: Markov, Chebyshev, Kolmogorov (probability), Lyapunov, Arnold (general nath), Lobachevskiy (geometry), Keldysh. They are all around. On the economy science, you could hear about Leontyev (A Nobel winner). And more not so well known. They were genuinely insightful, but, alas, sometimes, the politicians made them miserable, which can be a source of the bias. | |
| May 22, 2020 at 17:47 | comment | added | Aksakal | @SextusEmpiricus, that's all fair points, we don't know much about the actual data gathering process | |
| May 22, 2020 at 17:38 | comment | added | Sextus Empiricus | @Aksakal you assume that these numbers relate to the 8M tests and Binomial distribution with 4% incidence rate, but that may not need to be the case. The data have very little meta-information provided telling how the data is gathered. It can also be that the numbers relate to a secondary test which has some limit for the different regions (like around 100) and the region's are sending only their positive cases for second tests making the incidence rate very high. | |
| May 22, 2020 at 17:20 | comment | added | alexeymosco | @Aksakal, It is good to know, I was not familiar with this correlation of distributions. | |
| May 22, 2020 at 17:11 | comment | added | Aksakal | @AlexeyBurnakov, that yandex page shows me 8M tests and 326K infected, i.e. 4% incidence rate. So, Poisson should be a fairly Ok approximation | |
| May 22, 2020 at 16:52 | comment | added | alexeymosco | @Aksakal. I see, good point. By the way, upper in comments we already started treating the data as Binomial because case counts are fractions of tests made | |
| May 22, 2020 at 16:46 | comment | added | Aksakal | @AlexeyBurnakov, take a look at my updated answer. I scraped your Russia data, and it's over dispersed, the variance daily is very large. Kransodar krai data is "managed" one way or another | |
| May 22, 2020 at 16:36 | comment | added | alexeymosco | @Aksakal, I didn't measure variance or st.deviation for this plot. It wasn't the reason I posted it. It was to show that positive cases and tests are different processes. About 4% of tests resulted in cases. You just mentioned "tests". | |
| May 22, 2020 at 16:30 | comment | added | Aksakal | @AlexeyBurnakov, on #3, I think your plot for new cases in all Russia is not inconsistent with Poisson type of process. It shows 10k new cases daily, so the dispersion would be around 100, and that seems to be the case if you look at the fluctuation of daily new cases | |
| May 22, 2020 at 15:13 | comment | added | Sextus Empiricus | @AlexeyBurnakov in a comment under my answer I explain why I do not believe that it is some kind of intentional data manipulation of fabrication. Or at least the manipulation is not done by a single person. For that to be true the different regions look too much different in the way that they are fabricated. What I imagine is that it could be some sort of procedural limitation for the regions that turns this into binomial distributed data with high $p$. For instance, the regionally observed positive cases are being double checked, and the double checking is done in daily batches of fixed size | |
| May 22, 2020 at 15:00 | comment | added | alexeymosco | @SextusEmpiricus. I see now that limiting the number of tests is unlikely to flatten the data. It is hard to image that, for example, $p$ if a function tests $n$. Yes, agreed. Then, the source of low var/mean can be a data manipulation, but I don't what kind of it. It can be just "dispersing" counts more evenly over time or worse. Thank you for the discussion. | |
| May 22, 2020 at 14:45 | comment | added | Sextus Empiricus | @AlexeyBurnakov what we know is that if these data are binomial distributed with a small value for $p$, then we should not observe the noise/signal ratio that we observe. Sure the number $n$ might not be equal from day to day (and so is the number $p$ not equal from day to day). But the variations that may occur in $n$ and $p$ are not gonna be of the kind that smoothen the data. So let's get back (after long discussion) to the point 3 in your post. You suggest that the number of tests is somehow limited, but that does not explain the low signal/noise ratio. | |
| May 22, 2020 at 14:34 | comment | added | alexeymosco | @SextusEmpiricus, I understand. I cannot completely agree this is applicable here. Binomial experiments imply we do $n$ trials lots of times, right? The number of experiments are the number of days. If, indeed, we knew, $n$ is equal each time (without even knowing $n$), then, I agree, we couldn't go without bias. But we don't know if $n$ is equal. Do you see this is logical? HOWEVER, even if $n$ is not known and striclty speaking Binomial is also misleading, I can imagine that varying $n$ is not likely to produce low-variance results, it should, instead, increase the variance. So, I agree. | |
| May 22, 2020 at 14:01 | comment | added | Sextus Empiricus | Note that for a binomial distribution we have: $$\text{mean} = np$$ $$\text{variance} = np(1-p)$$ and $$\frac{\text{variance}}{\text{mean}} = 1-p \, \underbrace{\approx 1}_{\llap{\text{if $p$ }}\rlap{\text{close to 0}}}$$ So if $p$ is small (approximately 5% as you say) then it doesn't matter much what it is exactly and variance/mean ~ 1. | |
| May 22, 2020 at 13:55 | comment | added | Sextus Empiricus | @AlexeyBurnakov we do not need to know the exact numbers in the binomial case. It could be n=2000 or n=500, it doesn't matter. If $p$ is small (or equivalently $n$ large) then the variance and expected value are approximately equal (in fact you could approximate the binomial data with a Poisson distribution en.wikipedia.org/wiki/Poisson_limit_theorem). Only if you have some weird situation that p is very high >0.9 does the ratio noise/signal makes sense. I mentioned before a situation how this could happen. | |
| May 22, 2020 at 13:52 | comment | added | Sextus Empiricus | @Wrzlprmft I am not so much worried about overdispersion. It is more that the figures are heavily underreporting the true number of cases. It is not unthinkable that the degree of underreporting may change in time (the curve for China shows this clearly with a sudden bump when the test protocol was changed). So the curve will show patterns that partly reflect how we test and report. It is like using a very bad thermometer that is not showing the accurate temperature and neither consistent. It is the worse case of the four options. | |
| May 22, 2020 at 13:48 | comment | added | alexeymosco | @SextusEmpiricus, why? It is easy. We don't know how many tests ($n$) were done each day in the Krasnodar region. This info is absent. We only know that in whole country the proportion of positives ($k$) to tests is about 0.05. If we knew daily stats not only on positives, but also on tests, we could legitimately try Binomial. That's what I have just wrote. | |
| May 22, 2020 at 13:47 | comment | added | Sextus Empiricus | "It may be that the proportion would fluctuate more if exact test numbers were given." The numbers that we are currently looking at are not exact test numbers and not numbers that are daily updated? | |
| May 22, 2020 at 13:46 | comment | added | Wrzlprmft | @SextusEmpiricus: My point is that there are plenty of mechanisms that explain overdispersion. This does not automatically invalidate the data. Of course, one should not get overexcited over a sudden jump from one day to the next, but when you account for such effects and look at a proper moving average, the data can still have some value. By contrast, all mechanisms leading to underdispersion I can think of also lead to completely useless data. | |
| May 22, 2020 at 13:45 | comment | added | Sextus Empiricus | "But bear in mind that I referred to a country-wide figure." what does that mean in relation to my comment about the binomial distribution still having variance and expectation value being approximately the same? | |
| May 22, 2020 at 13:42 | comment | added | Sextus Empiricus | @AlexeyBurnakov I do not understand what you mean. What I got from your text is that you meant to say that the figure of 100 positive cases/day stems from something like 2000 tests/day. This indeed may explain why you have a plateau value. But... it does not explain why you have such little variation in the numbers. If your tests are limited to, say 2000, and if the expectation value is 100 then you should still expect a standard deviation around roughly 10. The data is heavily underdispersed if it comes from a binomial distribution with low $p$. (but if $p$ is large then it makes sense). | |
| May 22, 2020 at 13:37 | comment | added | alexeymosco | @SextusEmpiricus, the point about binomial distribution makes sense. Then, yes, low variance observed is strange as well. But bear in mind that I referred to a country-wide figure. We don't have daily test counts reported publicly, and by region. It may be that the proportion would fluctuate more if exact test numbers were given. | |
| May 22, 2020 at 13:28 | comment | added | Sextus Empiricus | "but that means that the numbers are actually not reflecting reality and thus suspicion is justified." we can already expect that the numbers do not reflect reality without the observation of underdispersion. The entire world goes crazy about these figures that are daily reported and overly dispersed among the many different media, while they are not that much accurate (many countries have limited testing capabilities). | |
| May 22, 2020 at 13:20 | comment | added | Wrzlprmft | There may be some dispersity-lowering mechanisms on the reporting level, but that means that the numbers are actually not reflecting reality and thus suspicion is justified. Moreover, as elaborated by @SextusEmpiricus, even limited testing capacities cannot explain this. The only thing I can think of is a bottleneck in the handling of reports, e.g., the office can at most handle 99 reports a day. But in that case, the data is indeed pretty useless. | |
| May 22, 2020 at 13:19 | comment | added | Wrzlprmft | Why Poisson? Cases generation process is intristically interdependent as a pandemic interaction between ill and healthy – Sure, the Poisson process is a rough assumption, but, when it comes to investigating underdispersion, it is a benign one. Most interdependency mechanisms such as superspreaders, weekends, weather would increase the dispersion in comparison to a Poisson process. I cannot think of any epidemiological mechanism that would decrease the dispersion. … | |
| May 22, 2020 at 11:54 | comment | added | Sextus Empiricus | .....For most situations with countdata we should expect that the variance and mean are roughly equal. Only when you have something like a binomial distributed variable with large value for $p$, then this is not the case. (I imagine this could be the case here when the reports are based on second opinion tests from a central lab where there is some limited number of testing capacity) | |
| May 22, 2020 at 11:54 | comment | added | Sextus Empiricus | @AlexeyBurnakov if you have each day 2000 tests out of which each test has a 5% probability to be positive, then you have something like a binomial distributed value (with $n = 2000$ and $p=0.05$) for which the expectation value, $np$ and variance $np(1-p)$ are still very close (it explains why you may get on average 100 tests, but not why you get 100 with so little variation) .... | |
| May 22, 2020 at 11:32 | comment | added | EngrStudent | @AlexeyBurnakov - the "Diamond Princess" data is nearly pristine. The demographics are a little older. (nature.com/articles/d41586-020-00885-w) The challenge then is a dynamic system model that transforms that non-cylic phenomenology to the complicated stuff we see. | |
| May 22, 2020 at 11:30 | comment | added | alexeymosco | @ttnphns, yes, true. And other tourist-dependent regions also relax carantine regime, like Turkey, Italy and may be some more. | |
| May 22, 2020 at 11:23 | comment | added | ttnphns | According to yesterday's news, Krasnodar region (1) is appointed to still open the tourism season from July (the region is a major sea-side resort); (2) isolation regime to be considerably relaxed from tomorrow. These facts ought to taken into account because the authorities have been starting some activities to meet the plans. These actions might but not necessarily imply some sort of falcification of numbers. They, however, would imply a definitely non-Poissonian process of "daily confirmed cases". | |
| May 22, 2020 at 11:22 | comment | added | alexeymosco | @EngrStudent, I agree with this. But it makes data looking strange, violating what we know about true distributions. Flattening case counts is also possible to cause underdispersion and it is also making data strange. And I agree that it can be a manupulation, but also can be due to the lack of medical workforce (a huge problem, doctors have been working extra shifts everywhere), and budget restricting number of tests made. | |
| May 22, 2020 at 11:17 | comment | added | EngrStudent | Daily pattern might come from several things: work-week vs. weekend worker activity/recreation, doctor hours(typically not weekend), reporting updates timing, lab/facilities operating hours | |
| May 22, 2020 at 11:14 | comment | added | EngrStudent | @AlexeyBurnakov - I would weep were that to happen. I was taught partial differential equations by Basil Nikolaenko. He managed 2 teams at NASA, one American calculator drivers and another immigrant Russian pencil users and he said when the immigrant group came to him with something their stuff was always right. I respect Russian mathematics greatly. I don't know about Russian economics either way though. | |
| May 22, 2020 at 11:09 | comment | added | alexeymosco | @EngrStudent, I would never like to see or get engaged in data politicizing on this website that I like. Not to mention that in the Soviet Union the statistics and economic science was very sophisticated. On your other two comments, intuitively, the data generation process is dependent, and data that I saw was always strange, non random. | |
| May 22, 2020 at 11:05 | history | edited | alexeymosco | CC BY-SA 4.0 |
added research
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| May 22, 2020 at 10:50 | comment | added | alexeymosco | 1) and 2). I don't see why underdispersion should be mentioned if you are not sure these are Poisson data. That was the point. 3) I mean there are on average 5 out of 100 people who were covid-positives after taking tests, so 100 positives mean 100 * 20 tests on average... That can really be a huge number of tests for a small region like Krasnodar and the test number can be limited to 2000 by budget constraints of lack of medical workers. 4) Let me add some research to my answer, you may be right. | |
| May 22, 2020 at 10:46 | comment | added | Sextus Empiricus | The point is that the data is under-dispersed. Even despite your point (1) and (2) one should expect that the variance of the noise in the data should be close to the mean of the data (or larger/overdispersed). This is also obvious from the plot of the curves where we see the odd drastic decrease in noise in May. (3) "With this, you should expect at least 2,000 tests per day allowed" what do you mean by that? (4) The world data has no low variance. It ranges from 80k to 100k. So roughly a coefficient of variation of some 10%. That is overdispersion not underdispersion. | |
| May 22, 2020 at 10:29 | comment | added | EngrStudent | I don't know that the world is Soviet, but I do know that modern politicians are filtered for two skillsets: stage appeal (good con-man) and fund raising (good sell-out). I don't know that the Poisson process actually captures the physics of the phenomena. I don't see contact tracing on the social graph, viral load, or any of that. | |
| May 22, 2020 at 9:34 | history | answered | alexeymosco | CC BY-SA 4.0 |